The Raspberry Pi is a good choice. I suggest you use the Raspbian operating system (it's a Linux based on Debian, so there is masses of free software for it). Raspbian has a big advantage over other alternatives - it is compiled specifically for the ARM processor in the Pi, so it gets the most out of the hardware.
Here's where to get a WiFi module for your Pi http://www.adafruit.com/products/814
Here's instructions for how to get the WiFi working http://www.raspberryshake.com/raspberry-pi-wireless-network-setup/
The Pi is a good choice in other ways - for instance, it has GPIO pins which enabe you to attach it to other electronics to control the circuits or read sensors, whatever. Here comes the good bit - these pins are programmable with Python (pretty much the easiest programming language to begin with, works fine on a Pi).
If you start by following the Paspberry Pi Foundation's website (http://www.raspberrypi.org/), you can get links to downlaod Raspbian, links to the Raspberry Pi wiki, the forums where you can ask for help, and lots of ideas from other people.
EDIT: I forgot to say, they've just announced a camera module for the Raspberry Pi - you could take a photo of everyone who comes to the front door, for security purposes...